CARACAS, Feb 24 (Reuters) - Venezuelan protest leader Leopoldo Lopez is being held alone in a small cell at a military jail but remains strong and wants his supporters to stay in the streets, his family says.

The wife and parents of Lopez, who was arrested last week as the alleged mastermind of unrest against President Nicolas Maduro's government, spoke after several visits to the hilltop Ramo Verde jail outside Caracas.

"He's isolated from everyone, he has no communication, no radio, TV or telephone. His only contact is with the family," his wife Lilian Tintori, 36, told Reuters at the headquarters of Lopez's political party Popular Will in Caracas on Monday.

"He's in a two-by-three (meter) cell with a small toilet. They don't let him out. The treatment is minimal: they bring food in the morning, midday and at night. It's a military jail, and the soldiers are following orders."

Tintori, a former TV presenter and sportswoman who has two young children with Lopez, has kept him informed of events outside and Tweets his messages to supporters.

The hardline opposition leader, a Harvard-educated economist, spearheaded street protests from the start of February that have grown around Venezuela.

At least 13 people have died in the most protracted unrest in Venezuela for a decade, leading Maduro to declare Lopez responsible for the violence.

The government has said Lopez will be treated humanely, but has not given details of his jail conditions.

"He's strong, he's firm," added Tintori, who was cheered by residents as she jumped on the back of a motorbike and drove through a burning barricade to a rally after the interview.

"He's convinced of what he said before surrendering, that if his imprisonment helps wake up Venezuela, then it's worth it ... His message is 'don't give up, this a dictatorial government and we have to keep up our peaceful protests, we mustn't be afraid, we're on the right side of history.'"

'SO PROUD ... SO SAD'

Tintori and Lopez's parents spoke in his office premises, where photos of heroes from Nelson Mandela and Mahatma Gandhi to Martin Luther King and Mother Teresa decorate the walls. Young party activists manned a call-center taking latest information about trouble and detentions around the country.

Leopoldo Lopez senior, 69, welled up with emotion talking about his son. "As a father, I'm so proud because he's doing what he has to do, and representing our family values. On the other hand, I'm so sad at the injustice he's living. In a democracy, you do not jail people for thinking differently."

The family have taken him a table and chair to complement the bed in his cell, plus coffee and dry fruit, his father said.

Lopez's one-year-old baby son Leopoldo Santiago, has been unwell and unable to visit him, but his daughter Manuela, 4, has seen him and thinks he's simply working.

"We told her he was doing military exercise," his father said. "She asked about the bars, and we said 'Well, in that place, there are lots of animals, lions and tigers, so he has to protect himself so they don't eat him.'"

Fluent in English and from a wealthy family, Lopez represents a radical opposition wing that believes street action is the only option because creeping authoritarianism makes democratic change of government impossible.

While treated as a hero in the wealthy Chacaco district of Caracas where he lives and was once mayor, he has not been able to ignite poorer sectors against Maduro.

The government paints him as a dangerous maverick and frequently reminds Venezuelans of his role in a short-lived 2002 coup against Chavez when Lopez even helped arrest a minister and haul him through a mob.

NO NEGOTIATIONS

Lopez's family said the government had offered him an exile deal, but that was out of the question.

Powerful Congress head Diosdado Cabello helped to arrange Lopez's surrender last week, but that was purely to ensure his physical safety, not as part of a negotiation, they insist.

"The treatment of him has been respectful, though for someone used to be in crowds daily, being alone and only able to talk to a jailer, is a form of mistreatment," his father said.

Maduro, and not Lopez, should be taking responsibility for the unrest and discontent across Venezuela, his family said, citing crime, queues, shortages and inflation.

"Those are the reasons why people are in the street. Leopoldo's was perhaps the most powerful and convincing cry, but the people were already in the street," Leopoldo Lopez senior said. "They're in serious trouble. Jailing him has simply convinced people that the reasons for being out were valid."

Lopez, whom his parents say was just six years old when he first told friends he wanted to grow up to be president, was initially arrested on charges including terrorism and murder.

They have been reduced to lesser counts of instigating arson, damage and criminal gatherings, that could bring a 10-year sentence. His family called the charges "absurd".

In his absence, Tintori has taken a more prominent role, appearing at opposition rallies to denounce Maduro's "dictatorship."

"The nights are the most difficult," she said. "But as I've said from day one, my bed may be empty but it's full of Venezuelans because of the support we've received, from the opposition and even from some 'Chavistas' who do not agree with his jailing, has been incredible. We'll fight to the end." (Editing by Kieran Murray)

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